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RU-ALLRUSSIAN 1963 Problem 9

    Given a triangle ABC. Let the line through C parallel to the angle bisector of B meet the angle bisector of A at D, and let the line through C parallel to the angle bisector of A meet the angle bisector of B at E. Prove that if DE is parallel to AB, then CA=CB\mathrm{CA} = \mathrm{CB} .

    Dataset text NuminaMath olympiads. Quoted with source.

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